Nonergodic dynamics of a system of nuclear spins 1/2 with identical spin-spin coupling constants

The exact solution for the evolution of nuclear spin polarizations in a system with spin-spin coupling constant g identical for all spin pairs is obtained on the condition that only one (first) spin is polarized at zero time. It is shown that the polarization P ₁(t) of the first spin has the form of periodic time pulsations with the period 4π/g. In every period, the function P ₁(t) changes from its initial value P(0)=1 to 1/3 during the time on the order of t≈4π/Ng, if the number of spins N?1, and remains in the state P ₁(t)=1/3 virtually during the entire period. A simple classical model within the framework of mean-field theory explains the physical nature of the nonergodic dynamics of the system.